{
  "id": "2403.15904",
  "version": "v1",
  "published": "2024-03-23T18:17:46.000Z",
  "updated": "2024-03-23T18:17:46.000Z",
  "title": "On a relation between $λ$-full well-ordered sets and weakly compact cardinals",
  "authors": [
    "Gabriele Gullà"
  ],
  "categories": [
    "math.LO",
    "math.GN"
  ],
  "abstract": "We prove, via transfinite recursion, the existence, inside any linearly ordered set of appropriate regular cardinality $\\lambda$, of a particular kind of well-ordered subsets characterized by the property of $\\lambda$-fullness. Let $H$ be a set of regular cardinals: by using our results about well-ordered $\\lambda$-full sets we show that if $\\inf H$ is a weakly compact cardinal, then, for every LOTS $X$, $H$-compactness is equivalent to the nonexistence of gaps of types in $H$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-23T18:17:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "weakly compact cardinal",
      "full well-ordered sets",
      "appropriate regular cardinality",
      "regular cardinals",
      "transfinite recursion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}